{"paper":{"title":"Iterated limits for aggregation of randomized INAR(1) processes with Poisson innovations","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Fanni Ned\\'enyi, Gyula Pap, Matyas Barczy","submitted_at":"2015-09-17T07:26:00Z","abstract_excerpt":"We discuss joint temporal and contemporaneous aggregation of $N$ independent copies of strictly stationary INteger-valued AutoRegressive processes of order 1 (INAR(1)) with random coefficient $\\alpha\\in(0,1)$ and with idiosyncratic Poisson innovations. Assuming that $\\alpha$ has a density function of the form $\\psi(x)(1 - x)^\\beta$, $x\\in(0,1)$, with $\\lim_{x\\uparrow 1}\\psi(x) = \\psi_1 \\in(0,\\infty)$, different limits of appropriately centered and scaled aggregated partial sums are shown to exist for $\\beta\\in(-1,0)$, $\\beta = 0$, $\\beta\\in(0,1)$ or $\\beta\\in(1,\\infty)$, when taking first the "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1509.05149","kind":"arxiv","version":3},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}